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**Linear Equations in Two Variables Class 9 Questions And Answers **are provided here. These NCERT solutions are prepared by expert team at careers360 keeping in mind latest CBSE syllabus 2023. In this particular chapter, you will study linear equations in two variables of the type ax + by + c = 0 where a, b and c are the real numbers, and a and b both are not zero. Class 9 linear equations in two variables NCERT solutions are there to make your task easy while preparing for the exams.

This Story also Contains

- NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables
- Linear Equations in Two Variables Class 9 Questions And Answers PDF Free Download
- Linear Equations in Two Variables Class 9 Solutions - Important Formulae
- Linear Equations in Two Variables Class 9 NCERT Solutions (Intext Questions and Exercise)
- Linear Equations In Two Variables Class 9 NCERT Solutions - Summary
- NCERT Solutions for Class 9 - Subject Wise
- NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables - Key Features
- NCERT Books and NCERT Syllabus

This class 9 linear equations in two variables always comes with a good number of questions in competitive exams like the Indian National Olympiad (INO), National Talent Search Examination (NTSE). Linear equations in two variables class 9 NCERT solutions are designed in such a manner that a student can get maximum marks assigned to that particular question. NCERT solutions for class 9 are also available chapter wise which can be downloaded by clicking on the given link.

**Also Read :**

- NCERT Exemplar Solutions For Class 9 Maths Chapter 4
- Linear Equations in Two Variables Class 9 NCERT Chapter Notes

(a + b)

^{2}= a^{2}+ 2ab + b^{2}(a - b)

^{2}= a^{2}- 2ab + b^{2}(a + b)(a - b) = a

^{2}- b^{2}(x + a)(x + b) = x

^{2}+ (a + b)x + ab(x + a)(x - b) = x

^{2}+ (a - b)x - ab(x - a)(x + b) = x

^{2}+ (b - a)x - ab(x - a)(x - b) = x

^{2}- (a + b)x + ab(a + b)

^{3}= a^{3}+ b^{3}+ 3ab(a + b)(a - b)

^{3}= a^{3}- b^{3}- 3ab(a - b)(x + y + z)

^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy + 2yz + 2xz(x + y - z)

^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy - 2yz - 2xz(x - y + z)

^{2}= x^{2}+ y^{2}+ z^{2}- 2xy - 2yz + 2xz(x - y - z)

^{2}= x^{2}+ y^{2}+ z^{2}- 2xy + 2yz - 2xzx

^{3}+ y^{3}+ z^{3}- 3xyz = (x + y + z)(x^{2}+ y^{2}+ z^{2}- xy - yz - xz)x

^{2}+ y^{2}= 1/2 [(x + y)^{2}+ (x - y)^{2}](x + a)(x + b)(x + c) = x

^{3}+ (a + b + c)x^{2}+ (ab + bc + ca)x + abcx

^{3}+ y^{3}= (x + y)(x^{2}- xy + y^{2})x

^{3}- y^{3}= (x - y)(x^{2}+ xy + y^{2})x

^{2}+ y^{2}+ z^{2}- xy - yz - zx = 1/2 [(x - y)^{2}+ (y - z)^{2}+ (z - x)^{2}]

Free download **NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables **for CBSE Exam.

**Linear equations in two variables class 9 solutions Exercise: 4.1**

** Answer: **

Let the cost of a notebook be Rs * x * and that of a pen be Rs * y * .

According to the given condition: The cost of a notebook is twice the cost of a pen.

Thus,

Given :

Here , a=2, b=3 and c =

Given:

Here ,

a=1,

c = -10

Given :

Here , a= -2, b=3 and c = -6

Given :

Here , a= 1, b= -3 and c =0

Given :

Here , a=2, b= 5 and c =0

Given :

Here , a= 3, b=0 and c =2

Given :

Here , a=0, b= 1 and c = -2

Given :

Here , a=2, b= 0 and c = -5

** Class 9 maths chapter 4 question answer Exercise: 4.2 **

** Q1 ** Which one of the following options is true, and why? has

Given :

This equation is of a line and a line has infinite points on it and each point is a solution Thus, (iii) infinitely many solutions is the correct option.

** Q2 ** Write four solutions for each of the following equations:

(i) (ii) (iii)

(i) Given :

Putting x=0, we have , means is a solution.

Putting x=1, we have , means is a solution.

Putting x=2, we have , means is a solution.

Putting x=3, we have , means is a solution.

The four solutions are : .

(ii) Given :

Putting x=0, we have , means is a solution.

Putting x=1, we have , means is a solution.

Putting x=2, we have , means is a solution.

Putting x=3, we have , means is a solution.

The four solutions are : .

(iii) Given :

Putting x=0, we have , means is a solution.

Putting x=1, we have , means is a solution.

Putting x=2, we have , means is a solution.

Putting x=3, we have , means is a solution.

The four solutions are : , , and .

** Q3 (i) ** Check which of the following are solutions of the equation and which are not: ((0,2)

(i) Given :

Putting ,

we have ,

Therefore, is not a solution of .

** Q3 (ii) ** Check which of the following are solutions of the equation and which are not: (2,0)

Given :

Putting (2,0),

we have ,

Therefore, (2,0) is not a solution of .

** Q3 (iii) ** Check which of the following are solutions of the equation and which are not: (4,0)

Given :

Putting (4,0),

we have ,

Therefore, (4,0) is a solution of .

** Q3 (iv) ** Check which of the following are solutions of the equation and which are not:

Given :

Putting ,

we have ,

Therefore, is not a solution of .

** Q3 (v) ** Check which of the following are solutions of the equation and which are not: (1,1)

Given :

Putting (1,1) ,

we have ,

Therefore, (1,1) is not a solution of .

** Q4 ** Find the value of * k * , if , is a solution of the equation .

Given :

Putting (2,1),

we have ,

Therefore, k=7 for putting x=2 and y=1.

**Class 9 maths chapter 4 question answer Exercise: 4.3 **

** Q1 (i) ** Draw the graph of each of the following linear equations in two variables:

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,4) and (1,3) are solutions of given equation.

** Q1 (ii) ** Draw the graph of each of the following linear equations in two variables:

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,-2) and (1,-1) are solutions of given equation.

** Q1 (iii) ** Draw the graph of each of the following linear equations in two variables:

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,0) and (1,3) are solutions of given equation.

** Q1 (iv) ** Draw the graph of each of the following linear equations in two variables:

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,3) and (1,1) are solutions of given equation.

The equations of two lines passing through (2, 14) are given by :

There are infinite lines passing through (2, 14) because infinite lines pass through a point.

** Q3 ** If the point (3, 4) lies on the graph of the equation , find the value of * a * .

Given : the point (3, 4) lies on the graph of the equation

Put x=3 and y=4

Given: The distance covered as x km and total fare is Rs. y.

Total fare =the fare for first km + the fare of the remaining distance

For graph,

Putting x=0, we have

Putting x=1, we have

Putting x=2, we have

Hence,(0,3),(1,8) and (2,13) are solutions of equation.

The graph is as shown :

** Q5 (A) ** From the choices given below, choose the equation whose graph is given in Fig. 4.6.

(i)

(ii)

(iii)

(iv)

For the given figure :

Points on line are (-1,1) , (0,0 ) and (1,-1)

satisfies all the above points.

Thus, is the correct equation of the line.

** Q5 (B) ** From the choices given below, choose the equation whose graph is given in Fig. 4.7

(i)

(ii)

(iii)

(iv)

For the given figure :

Points on line are (-1,3) , (0,2 ) and (2,0)

satisfies all the above points.

Thus, is the correct equation of the line.

Let work done be y and distance be x.

Given : Constant force = 5 units

Work done by a body on the application of a constant force is directly proportional to the distance travelled by the body.

i.e.

k=Constant force = 5

Then,

For graph,

Put x=0,we have

Put x=1,we have

Put x=2,we have

Points are (0,0) , (0,5) and (2,10)

If the distance travelled is 2 units then the work done is 10 units.

Let work done be y and distance be x.

Given : Constant force = 5 units

Work done by a body on the application of a constant force is directly proportional to the distance travelled by the body.

i.e.

k=Constant force = 5

Then,

For graph,

Put x=0,we have

Put x=1,we have

Put x=2,we have

Points are (0,0) , (0,5) and (2,10)

If the distance travelled is 0 units then work done is 0 units.

Let the contribution of Yamini be x.

contribution of Yamini be y.

According to question,

For x=0 , we have

For x=10 , we have

For x=20 , we have

Hence, (0,100) , (10,90) and (20,80)

Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis.

Let celsius be on x-axis and Fahrenheit be on y-axis.

For graph,

Putting x=0, we get

Putting x=5, we get

Putting x=10, we get

Hence, points are (0,32) , (5,41) and (10,50).

If the temperature is 30°C, what is the temperature in Fahrenheit?

Put c=30,

Thus, the temperature = 30°C, then the temperature is 86 in Fahrenheit.

If the temperature is 95°F, what is the temperature in Celsius?

Put F=95,

If the temperature is 95°F, then 35 is the temperature in Celsius.

If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?

If the temperature is 0°C,

if the temperature is 0°F,

Thus, if the temperature is 0°C , then the temperature in Fahrenheit is 32 and if the temperature is 0°F, then the temperature in celsius is -17.8.

(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Let temperature be x in both Fahrenheit and celsius.

Thus, 40 is the temperature which is numerically the same in both Fahrenheit and celsius.

** Class 9 maths chapter 4 NCERT solutions Exercise: 4.4 **

** Q1 (i) ** Give the geometric representations of as an equation

in one variable

Equation can be represented in one variable on the number line.

** Q1 (ii) ** Give the geometric representations of as an equation: in two variables

For 2 variable representations of .

Equation :

For graph,

x=0,we have y=3

x=1,we have y=3

x=2,we have y=3

Hence, (0,3) ,(1,3) and (2,3) are solutions of equation.

** Q2 (i) ** Give the geometric representations of as an equation: in one variable

Equation can be represented in one variable on the number line.

The yellow mark represents x= - 4.5.

** Q2 (ii) ** Give the geometric representations of as an equation: in two variables

For 2 variable representation of .

Equation :

For graph,

y=0,we have

y=1,we have

y=2,we have

Hence, , and are solutions of equation.

The chapter 4 maths class 9 Textbook is called "Linear Equations in Two Variables," which is included in Unit 2 Algebra. In the board exams, Algebra unit comprises a total of 20 marks, consisting of 1 multiple choice question for 1 mark, 2 short answers with reasoning for a total of 4 marks, 3 short answer questions for a total of 9 marks, and 1 long answer question for 6 marks. The chapter covers the following topics:

Chapter 4 | Linear Equations in Two Variables |

4.1 | Introduction |

4.2 | Linear Equations |

4.3 | Solution of a Linear Equation |

4.4 | Graph of a Linear Equation in Two Variables |

4.5 | Equations of Lines Parallel to the x-axis and y-axis |

In this class 9 chapter 4 maths, there are a total of 4 exercises which consist of 16 questions. NCERT solutions for Class 9 Maths chapter 4 Linear Equations in Two Variables is covering the detailed solutions to each and every question present in the practice exercises. This is an important chapter as this created a foundation for the higher level of algebra. Algebra is a unit in class 9 maths which holds 20 marks in the final examination.

Interested students can practice class 9 maths ch 4 question answer using the links given below.

- NCERT Solutions for Class 9 Maths Exercise 4.1
- NCERT Solutions for Class 9 Maths Exercise 4.2
- NCERT Solutions for Class 9 Maths Exercise 4.3
- NCERT Solutions for Class 9 Maths Exercise 4.4

NCERT Solutions for Class 9 Maths - Chapter Wise

Chapter No. | Chapter Name |

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | Linear Equations In Two Variables |

Chapter 5 | |

Chapter 6 | |

Chapter 7 | |

Chapter 8 | |

Chapter 9 | |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 | |

Chapter 14 | |

Chapter 15 |

**Comprehensive and Step-by-Step:** These maths chapter 4 class 9 solutions provide comprehensive coverage of the topic, presented in a step-by-step format for easy understanding.

**Practice-Driven:** They offer a variety of exercises, including illustrative examples and practical applications, along with additional practice questions to strengthen problem-solving skills.

**Accurate and Exam-Oriented:** The ch 4 maths class 9 solutions are accurate, exam-oriented, and readily accessible, making them an ideal resource for self-study and preparation for class assessments and board exams.

* Keep Working Hard & Happy Learning! *

1. What are the important topics in chapter Linear Equations in Two Variables ?

- Linear equations, solutions of linear equations
- The graph of linear equation in two variables,
- Equations of lines parallel to x-axis and y-axis are the important topics of this chapter.

2. Is it necessary to learn all the questions in linear equations in two variables questions?

Yes, practicing all the questions and formulas related to maths class 9 chapter 4 is essential to perform well in CBSE exams. Careers360 website provides accurate and easy-to-understand solutions, which can be beneficial for students to score higher marks. Apart from exam preparation, these solutions can also assist in solving homework and assignments. Therefore, students can start practicing NCERT Solutions for Class 9 Maths Chapter 4 to improve their overall performance.

3. Where can I find the complete class 9 maths chapter 4 solutions?

Here you will get the detailed NCERT solutions for class 9 maths by clicking on the link. you can practice linear equations class 9 NCERT solutions which provide you indepth understanding of concepts that ultimately lead to score well in the exam. Also for ease you can study linear equations in two variables class 9 pdf both online and offline mode.

4. How does the NCERT solutions are helpful ?

NCERT solutions are provided in a very detailed manner which will give the conceptual clarity to the students. Also, they can take help from these solutions if they are not able to solve on their own

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